Typically, a multipole mass filter (e.g., a quadrupole mass filter, alternately referred to herein as a “QMF”) may be used for mass analysis of ions provided within a continuous ion beam. For example, FIG. 6 is a cross sectional view through the four parallel rods of a quadrupole mass filter. A quadrupole field is produced within the quadrupole apparatus by dynamically applying electrical potentials on configured parallel rods arranged with four-fold symmetry about a long axis, depicted as piercing point 54, which comprises an axis of symmetry that is conventionally referred to as the z-axis. By convention, the four rods are described as a pair of “x rods” 51a, 51b and a pair of “y rods” 52a, 52b. At any instant of time, the two x rods have the same potential as each other, as do the two y rods. The potential on the y rods is inverted with respect to the x rods. The “x-direction” or “x-dimension” is taken along a line connecting the centers of the x-rods. The “y-direction” or “y-dimension” is taken along a line connecting the centers of the y-rods. The x rods 51a, 51b are diametrically opposed to one another with respect to an ion transmission volume 55. Likewise, the y rods 52a, 52b are diametrically opposed to one another with respect to the ion transmission volume. Each pair of rods consisting of one of the x rods and one of the y rods is referred to herein as a pair of adjacent rods. Thus each x rod is adjacent to both of the y rods and vice versa.
Relative to the non-time-varying potential along central the z-axis 54, the potential on each set of rods, as provided by power supply 53, can be expressed as a constant non-oscillatory (DC) offset (between point A and point B of FIG. 6) plus an oscillatory RF component that oscillates rapidly (with a typical frequency of about 1 MHz). The DC offset on the x-rods is positive so that a positive ion feels a restoring force that tends to keep it near the z-axis; the potential in the x-direction is like a well. Conversely, the DC offset on the y-rods is negative so that a positive ion feels an outward-directed force that drives it further away from the z-axis; consequently, the potential in the (x, y) plane that is normal to the z-axis is in the form of a saddle.
In operation of a quadrupole mass filter, an oscillatory RF component is applied to both pairs of rods. The RF phase on the x-rods 51a, 51b is the same and differs by 180 degrees from the phase on the y-rods 52a, 52b. Ions move inertially along the z-axis 54 from an entrance or inlet end of the quadrupole to a detector often placed at an opposite outlet of the quadrupole. Inside the quadrupole, ions have trajectories that are separable in the x and y directions. In the x-direction, the applied RF field carries ions with the smallest mass-to-charge (m/z) ratios out of the potential well and into the rods. Ions with sufficiently high mass-to-charge ratios remain trapped in the well and have stable trajectories in the x-direction. The applied field in the x-direction thus acts as a high-pass mass filter. Conversely, in the y-direction, only the lightest ions are stabilized by the applied RF field, which overcomes the tendency of the applied DC to pull them into the rods. Thus, the applied field in the y-direction acts as a low-pass mass filter. Ions that have both stable component trajectories in both x- and y-directions pass through the quadrupole so as to reach an ion detector.
In operation, the DC offset and RF amplitude applied to a quadrupole mass filter is chosen so as to transmit only ions within a restricted range of mass-to-charge (m/z) ratios through the entire length of the quadrupole. Such apparatuses can be operated either in the radio frequency (RF)-only mode or in an RF/DC mode. Depending upon the particular applied RF and DC potentials, only ions of selected m/z ratios are allowed to pass completely through the rod structures, whereas the remaining ions follow unstable trajectories leading to escape from the applied multipole field. When only an RF voltage is applied between predetermined electrodes, the apparatus serves to transmit ions in a wide-open fashion above some threshold mass. When a combination of RF and DC voltages is applied between predetermined rod pairs there is both an upper cutoff mass as well as a lower cutoff mass, such that only a restricted range of m/z ratios (i.e., a pass band) passes completely through the apparatus. As the ratio of DC to RF voltage increases, the transmission band of ion masses narrows so as to provide for mass filter operation, as known and as understood by those skilled in the art. As is further known, the amplitudes of the DC and RF voltages may be simultaneously varied, but with the DC/RF ratio held nearly constant so as to maintain a uniform pass band, such that the pass band is caused to systematically “scan” a range of m/z ratios. Detection of the quantity of ions passed through the quadrupole mass filter over the course of such scanning enables generation of a mass spectrum.
The motion of ions within an ideal quadrupole is modeled by the Mathieu equation. Solutions to the Mathieu equation are generally described in terms of the dimensionless Mathieu parameters, “a” and “q”, which are defined as:
            a      =                        8          ⁢                                          ⁢          e          ⁢                                          ⁢          U                          m          ⁢                                          ⁢                      r            0            2                    ⁢                      Ω            2                                ;        q    =                  4        ⁢                                  ⁢        e        ⁢                                  ⁢        V                    m        ⁢                                  ⁢                  r          0          2                ⁢                  Ω          2                    in which e is the charge on an electron, U is applied DC voltage, V is the applied zero-to-peak RF voltage, in is the mass of the ion, r is the effective radius between electrodes, and Ω is the applied RF frequency. General solutions of the Mathieu equation, i.e., whether or not an ion has a stable trajectory within a quadrupole apparatus, depend only upon these two parameters. The specific trajectory for a particular ion also depends on a set of initial conditions—the ion's position and velocity as it enters the quadrupole and the RF phase of the quadrupole at that instant.
As known to those skilled in the art, general solutions of the Mathieu equation can be classified as bounded and non-bounded. Bounded solutions correspond to trajectories that never leave a cylinder of finite radius, where the radius depends on the ion's initial conditions. Typically, bounded solutions are equated with trajectories that carry the ion through the quadrupole to the detector. The plane of (q, a) values can be partitioned into contiguous regions corresponding to bounded solutions and unbounded solutions, as shown in FIG. 1. Such a depiction of the bounded and unbounded regions in the q-a plane is called a stability diagram. The region containing bounded solutions of the Mathieu equation is called a stability region and is labeled “X & Y Stable” in FIG. 1. A stability region is formed by the intersection of two regions, corresponding to regions where the x- and y-components of the trajectory are stable respectively. There are multiple stability regions, but conventional instruments involve the principal stability region. By convention, only the positive quadrant of the q-a plane is considered. In this quadrant, the stability region resembles a triangle, as illustrated in FIG. 1.
Dashed and dashed-dotted lines in FIG. 1 represent lines of iso-βx and iso-βy, respectively, where the Mathieu parameters βx and βy are related to ion oscillation frequencies, ωx and ωy, in the x- and y-directions, respectively. The region of ion-trajectory stability in the y-direction lies to the right of the curve labeled βy=0.0 in FIG. 1, which is a bounding line of the stability region. The region of ion-trajectory stability in the x-direction lies to the left of the curve labeled βx=1.0 in FIG. 1, which is a second bounding line of the stability region. If an ion's trajectory is unstable in either the x-direction or the y-direction, then that ion cannot be transmitted through the quadrupole mass filter.
During common operation of a quadrupole for mass analysis (scanning) purposes, the instrument may be “scanned” by increasing both U and V amplitude monotonically to bring different portions of the full range of m/z values into the stability region at successive time intervals, in a progression from low m/z to high m/z. A special case occurs when U and V are each ramped linearly in time. In this case, all ions progress along the same fixed “scan line” through the stability diagram, with ions moving along the line at a rate inversely proportional to m/z. Two such scan lines are illustrated in FIG. 1. A first illustrated scan line 1 passes through the stability region boundary points 2 and 3. A second illustrated scan line 3 passes through the boundary points 6 and 8. The width of the m/z pass band of a quadrupole mass filter decreases as the scan line is adjusted to pass through the stability region more closely to the apex, said apex defined by the intersection of the curves labeled βy=0.0 and βx=1.0 in FIG. 1. During conventional mass scanning operation, the voltages U and V are ramped proportionally in accordance with a scan line that passes very close to the apex, thus permitting only a very narrow pass band that moves through the m/z range nearly linearly in time. Thus, during such conventional operation, the flux of ions hitting the detector as a function of time is very nearly proportional to the mass distribution of ions in a beam and the detected signal is a “mass spectrum”.
Typically, quadrupole mass filters are employed as a component of a triple stage mass spectrometer system. By way of non-limiting example, FIG. 2 schematically illustrates a triple-quadrupole system, as generally designated by the reference numeral 10. The operation of mass spectrometer 10 can be controlled and data 68 can be acquired by a control and data system (not depicted) of various circuitry of one or more known types, which may be implemented as any one or a combination of general or special-purpose processors (digital signal processor (DSP)), firmware, software to provide instrument control and data analysis for mass spectrometers and/or related instruments. A sample containing one or more analytes of interest can be ionized via an ion source 52 operating at or near atmospheric pressure. By way of non-limiting example, FIG. 2 illustrates an ion source in which ionization is effected through the use of an electrospray nozzle 55 that receives a liquid sample from a chromatograph capillary 51. The resultant ions are directed via predetermined ion optics that often can include tube lenses, skimmers, and multipoles, e.g., reference characters 53 and 54, so as to be urged through a series of chambers, e.g., chambers 22, 23 and 24, of progressively reduced pressure that operationally guide and focus such ions to provide good transmission efficiencies. The various chambers communicate with corresponding evacuation ports 80 (represented as arrows in FIG. 2) that are coupled to a set of vacuum pumps (not shown) to maintain the pressures at the desired values.
The example mass spectrometer system 10 of FIG. 2 is shown illustrated to include a triple stage configuration 64 within a high vacuum chamber 25, the triple stage configuration having sections labeled Q1, Q2 and Q3 electrically coupled to respective power supplies (not shown). The Q1, Q2 and Q3 stages may be operated, respectively, as a first quadrupole mass filter, a fragmentation cell, and a second quadrupole mass filter. Ions that are either filtered, filtered and fragmented or fragmented and filtered within one or more of the stages are passed to a detector 66. Such a detector is beneficially placed at the channel outlet of the quadrupole (e.g., Q3 of FIG. 2) to provide data that can be processed into a rich mass spectrum (data) 68 showing the variation of ion abundance with respect to m/z ratio.
During conventional operation of a multipole mass filter, such as the quadrupole mass filter Q3 shown in FIG. 2, to generate a mass spectrum, a detector (e.g., the detector 66 of FIG. 2) is used to measure the quantity of ions that pass completely through the mass filter as a function of time while the RF and DC voltage amplitudes are scanned as described above. Thus, at any point in time, the detector only receives those ions having m/z ratios within the mass filter pass band at that time—that is, only those ions having stable trajectories within the multipole under the particular RF and DC voltages that are applied at that time. Such conventional operation creates a trade-off between instrument resolution (or instrument speed) and sensitivity. High mass resolving can be achieved, but only if the DC/RF ratio is such that the filter pass band is very narrow, such that most ions develop unstable trajectories within the mass filter and few pass through to the detector. Under such conditions, scans must be performed relatively slowly so as to detect an adequate number of ions at each m/z data point. Conversely, high sensitivity or high speed can also be achieved during conventional operation, but only by widening the pass band, thus causing degradation of m/z resolution.
U.S. Pat. No. 8,389,929, which is assigned to the assignee of the present invention and which is incorporated by reference herein in its entirety, teaches a quadrupole mass filter method and system that discriminates among ion species, even when ions of various mass-to-charge ratios are simultaneously stable, by recording where the ions strike a position-sensitive detector as a function of the applied RF and DC fields. When the arrival times and positions are binned, the data can be thought of as a series of ion images. Each observed ion image is essentially the superposition of component images, one for each distinct m/z value exiting the quadrupole through its outlet end at a given RF phase point. The same patent also teaches methods for the prediction of an arbitrary ion image as a function of m/z and the applied field. Thus, using the predicted images as basis vectors, the image pattern for each individual m/z species within an unknown sample can be extracted from a sequence of observed ion images by a mathematical deconvolution or decomposition processes, as further discussed in the patent. The mass-to-charge ratio and abundance of each species necessarily follow directly from the deconvolution or decomposition.
The inventors of U.S. Pat. No. 8,389,929 recognized that ions of differing m/z ratios exiting a quadrupole mass filter may be discriminated, even when the ions of the differing m/z ratios are simultaneously stable (that is, have stable trajectories) within the mass filter, by recording where the ions strike a position-sensitive detector as a function of the applied RF and DC fields. The inventors of U.S. Pat. No. 8,389,929 recognized that such operation is advantageous because when a quadrupole is operated in, for example, a mass filter mode, the scanning of the device (that is provided by ramped RF and DC voltages) naturally varies the spatial characteristics with time as observed at the exit aperture of the instrument. Specifically, ions manipulated by a quadrupole are induced to perform a complex 2-dimensional oscillatory motion on the detector cross section as the scan passes through the stability region of the ions. The ion motion (i.e., for a cloud of ions of the same m/z but with various initial displacements and velocities) may be characterized by the variation of a and q, this variation influencing the position and shape cloud of ions exiting the quadrupole. For two masses that are almost identical, the sequence of their respective oscillatory motions is essentially the same and can be approximately related by a time shift.
The aforementioned U.S. Pat. No. 8,389,929 teaches, inter alia, a mass spectrometer instrument having both high mass resolving power and high sensitivity, the mass spectrometer instrument including: a multipole configured to pass an abundance of one or more ion species within stability boundaries defined by applied RF and DC fields; a detector configured to record the spatial and temporal properties of the abundance of ions at a cross-sectional area of the multipole; and a processing means. The data acquired by the so-configured detector can be thought of as a series of ion images. Each observed ion image is essentially the superposition of component images, one for each distinct m/z value exiting the quadrupole at a given time instant. The aforementioned patent also provides for the prediction of an arbitrary ion image as a function of m/z and the applied field. As a result, each individual component can be extracted from a sequence of observed ion images by mathematical deconvolution or decomposition processes which generate the mass-to-charge ratio and abundance of each species. Accordingly, high mass resolving power may be achieved under a wide variety of operating conditions, a property not usually associated with quadrupole mass spectrometers.
The teachings of the aforementioned U.S. Pat. No. 8,389,929 exploit the varying spatial characteristics by collecting the spatially dispersed ions of different m/z even as they exit the quadrupole at essentially the same time. FIG. 3 shows a simulated recorded image of a particular pattern at a particular instant in time. The example image can be collected by a fast detector, (i.e., a detector capable of time resolution of 10 or more RF cycles, more often down to an RF cycle or with sub RF cycles specificity, where said sub-RF specificity is possibly averaged for multiple RF cycles), positioned to acquire where and when ions exit and with substantial mass resolving power to distinguish fine detail.
The aforementioned patent described the use of three independent dimensions of acquired data to decompose a composite mass spectrum into its individual components and, by so doing, produce a high quality mass spectrum of ions exiting a mass filter at each time point in a mass scan. The three dimensions described in the patent are the two spatial (x and y) dimensions at the exit plane of a quadrupole and a third dimension comprising sub-RF phase within an RF cycle, which is referred to as sub-RF sampling. Each three-dimensional data structure was called a “voxel set” and each data point in time along a mass axis that is sampled has a corresponding voxel set data structure associated with it.
The inventors of the present invention have recognized that, since the mathematical deconvolution process described in the aforementioned patent admits of any number of dimensions of data, the acquisition of data according to additional independent variables can augment the information relating to each ion species and can enable further differentiation of different ion species from one other. Thus, the terminology “voxel set”, as used in this application, refers to a multidimensional data set and is a generalization of the common term “voxel” (i.e., a volumetric pixel) to any number of dimensions of data. The inventors have further recognized and here teach that there is a simple way to collect the additional information relating to each ion using the same detection systems that are described in the above-referenced patents and patent applications.